Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds

Details Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds

2007-09-04

arxiv.org/abs/0709.0467v2

J. London Math. Soc., 79(2), 346-362, 2009

Mathematics

Algebraic Geometry

19 pages; updated first part of arXiv:0709.0467v1 containing the results on small deformations. The results on deformations in

Scientific paper

10.1112/jlms/jdn076

We consider nilmanifolds with left-invariant complex structure and prove that small deformations of such structures are again left invariant if the Dolbeault-cohomology of the nilmanifold can be calculated using left-invariant forms. By a result of Console and Fino this is generically the case. Our main tool is an analog of Dolbeault-cohomology for Lie-algebras with complex structure.

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